HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 591 · 40 questions

How to solve it (Together again or cut equally?): “Ring together again”, “smallest number both divide” → LCM: count in the bigger number until the smaller one divides it. “Longest equal pieces”, “greatest number of identical packs” → HCF: list the factors and pick the greatest common one. Check: the LCM is divisible by both numbers; the HCF divides both numbers.

1. 1.Two ribbons are 35 cm and 40 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 1 cm (b) 35 cm (c) 280 cm (d) 5 cm
2. 2.Two ribbons are 6 cm and 21 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 15 cm (b) 1 cm (c) 3 cm (d) 6 cm
3. 3.A teacher has 8 pencils and 12 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 2 (c) 4 (d) 8
4. 4.Two ribbons are 6 cm and 14 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 2 cm (b) 1 cm (c) 8 cm (d) 6 cm
5. 5.Two ribbons are 8 cm and 14 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 6 cm (b) 1 cm (c) 2 cm (d) 8 cm
6. 6.Two bells ring every 6 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 21 min (b) 30 min (c) 3 min (d) 90 min
7. 7.Two bells ring every 18 minutes and every 24 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 42 min (b) 432 min (c) 6 min (d) 72 min
8. 8.Two bells ring every 18 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 126 min (b) 3 min (c) 378 min (d) 39 min
9. 9.Two ribbons are 12 cm and 27 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 12 cm (b) 15 cm (c) 1 cm (d) 3 cm
10. 10.What is the smallest number of sweets that can be shared equally among 16 children or among 28 children, with none left over? (a) 112 (b) 448 (c) 224 (d) 44
11. 11.Two ribbons are 14 cm and 35 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 21 cm (b) 1 cm (c) 7 cm (d) 14 cm
12. 12.Two ribbons are 20 cm and 25 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 20 cm (b) 5 cm (c) 1 cm (d) 100 cm
13. 13.A teacher has 60 pencils and 96 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 36 (c) 12 (d) 60
14. 14.What is the smallest number of sweets that can be shared equally among 12 children or among 28 children, with none left over? (a) 84 (b) 40 (c) 168 (d) 336
15. 15.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 24 (b) 135 (c) 90 (d) 45
16. 16.A teacher has 27 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 108 (c) 27 (d) 3
17. 17.What is the smallest number of sweets that can be shared equally among 6 children or among 15 children, with none left over? (a) 90 (b) 60 (c) 30 (d) 21
18. 18.A teacher has 22 pencils and 77 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 55 (b) 11 (c) 1 (d) 22
19. 19.Two ribbons are 28 cm and 35 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 28 cm (b) 1 cm (c) 140 cm (d) 7 cm
20. 20.Two bells ring every 18 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 540 min (b) 6 min (c) 48 min (d) 90 min
21. 21.What is the smallest number of sweets that can be shared equally among 20 children or among 28 children, with none left over? (a) 48 (b) 560 (c) 140 (d) 280
22. 22.Two ribbons are 16 cm and 24 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 16 cm (b) 48 cm (c) 8 cm (d) 4 cm
23. 23.Two ribbons are 24 cm and 108 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 84 cm (b) 12 cm (c) 6 cm (d) 24 cm
24. 24.What is the smallest number of sweets that can be shared equally among 8 children or among 10 children, with none left over? (a) 40 (b) 41 (c) 18 (d) 80
25. 25.A teacher has 32 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 8 (c) 32 (d) 4
26. 26.What is the smallest number of sweets that can be shared equally among 8 children or among 28 children, with none left over? (a) 36 (b) 56 (c) 112 (d) 224
27. 27.Two bells ring every 8 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 20 min (b) 96 min (c) 24 min (d) 4 min
28. 28.Two ribbons are 12 cm and 32 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 20 cm (b) 2 cm (c) 12 cm (d) 4 cm
29. 29.A teacher has 32 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 40 (b) 8 (c) 4 (d) 32
30. 30.What is the smallest number of sweets that can be shared equally among 12 children or among 18 children, with none left over? (a) 72 (b) 30 (c) 216 (d) 36
31. 31.Two ribbons are 8 cm and 10 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 8 cm (b) 2 cm (c) 40 cm (d) 1 cm
32. 32.Two bells ring every 20 minutes and every 24 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 44 min (b) 480 min (c) 120 min (d) 4 min
33. 33.Two bells ring every 15 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 35 min (b) 60 min (c) 5 min (d) 300 min
34. 34.Two ribbons are 4 cm and 14 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 1 cm (b) 10 cm (c) 4 cm (d) 2 cm
35. 35.What is the smallest number of sweets that can be shared equally among 18 children or among 24 children, with none left over? (a) 144 (b) 432 (c) 42 (d) 72
36. 36.Two bells ring every 4 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 14 min (c) 40 min (d) 20 min
37. 37.Two bells ring every 20 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 5 min (b) 55 min (c) 700 min (d) 140 min
38. 38.Two bells ring every 15 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 50 min (b) 5 min (c) 525 min (d) 105 min
39. 39.What is the smallest number of sweets that can be shared equally among 6 children or among 14 children, with none left over? (a) 20 (b) 42 (c) 43 (d) 84
40. 40.Two ribbons are 40 cm and 70 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 10 cm (b) 40 cm (c) 30 cm (d) 5 cm

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